"...I keep seeing Bell, Black, Bolton and Hanna. Ok, so who has these
books, and who can tell me what is says about the Scottish line of
Dundas?"

Who has them? People who do a lot of work in the fields of Scotch-Irish
genealogy and history. Along with a dozen or two others, they are
pretty much the standard reference works on the subject (you'll get some
argument on this, I expect, or I will). If you're thinking of acquiring
them, they are:

Robert Bell "The Book of Ulster Surnames",
George F. Black "The Surnames of Scotland",
Charles K. Bolton "Scotch-Irish Pioneers in Ulster and America", and
Charles A. Hanna "The Scotch-Irish".

They're available through any number of bookstores, including on-line
bookstores.

DUNDAS: One of the oldest historical Scottish names. According to
Black, it has been said of the House of Dundas that, "any prime minister
can raise a man to the House of Lords, but it takes seven centuries of
Scottish History to make a Dundas of Dundas". Black also says that the
Dundases of Virginia are descended from a Scot who emigrated there in
1757; he doesn't say "the Scot" went via Ulster, but he certainly could
have. The fact remains that at least one Virginia branch of the family
may be of Scottish, but not Scotch-Irish, ancestry.
Bell doesn't mention the name, indicating it's not among the 500
most common in Ulster. Bolton and Hanna, in describing Scotch-Irish
immigrants to America, don't mention the name. But in a chapter on
Ulster, Hanna reports that a Lieutenant Hugh Dundas was among those
ordered out of Ulster (to be resettled in Munster) after Cromwell's
victory at the battle of Worcestor in 1651. So they were there, at
least in small numbers.
None of the sources cited mention the Walter Dundas you mentioned,
but that certainly doesn't mean your information is incorrect; I'm sure
it's not. It simply means that an hours' research didn't turn him up.
The bottom line seems to be that in what's now the USA, Dundas is
certainly of Scottish origin, and may well be Scotch-Irish.